Development of Fragility Curves for Historical Masonry Buildings on Strip Foundations Exposed to Subsidence Using NLFE Models

Abstract

This paper presents a framework for developing fragility curves for masonry buildings on strip foundations exposed to subsidence using non-linear finite element (NLFE) analyses. A 2D plane-stress model of a masonry façade is used to evaluate the probability of cracking damage resulting from settlements. The model simulates the behaviour of typical Dutch two-storey historical buildings, using an established modelling approach to represent the non-linear behaviour of the façade, the transversal walls and the strip foundation, supported by a base interface for soil-foundation interaction. Settlements are imposed at the bottom of the interface, characterizing their intensity with the angular distortion. The damage severity is objectively quantified using the scalar parameter Ψ, computed considering the number, length, and width of the cracks. Cumulative probability functions are derived from 864 numerical analyses that account for realistic variations in building and soil features, including 3 masonry materials, 2 strip foundation systems, 2 interface soil materials and the 72 possible settlement patterns. The effect of each selected variation is evaluated individually. The proposed curves reveal a probability of over 25% for cracks up to 5 mm in width when the angular distortion equal to 0.2% (or 1/500), the threshold deemed acceptable by international codes, is applied to the models. Doubling the applied angular distortion results in an approximate doubling of the probability of damage. While the proposed curves are specific to the selected geometry, the framework can be adapted to accommodate different façade geometries, enabling the development of more comprehensive fragility functions.